On the Gonality type invariants and the slope of a fibered 3-fold

2024/04/08 by Hiroto Akaike, Akaike, Hiroto
Mathematics · #14J30 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Primary 14D06 #Secondary 14J10

paper · pdf · doi:10.48550/arxiv.2404.05216

openalex publication_date 2024/04/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The slope of a fibered 3-folds f:X → B is a relative numerical invariant defined by λ(f) := K_f³/deg(f_∗ω_f), where K_f is the relative canonical divisor and ω_f is the relative dualizing sheaf. Establishing slope inequalities is a fundamental problem in the geography of fibered spaces. In this paper, we introduce a new invariant called the minimal covering degree as a gonality-type invariant and study a lower bound of the slope increasing with the covering gonality and the minimal covering degree of the general fiber of f.

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